Topological phases of matter in open quantum systems: concrete frameworks and practical probes

Recent years have been marked by theoretical and experimental discoveries of novel states of matter that are characterized by topological features. Much of the excitement around these topological systems is due to their promise to quantum technologies, including EU strategic research priorities like quantum metrology, quantum sensing and imaging, quantum computing, quantum communication, and quantum simulation for material synthesis. Advancing these crucial quantum technologies requires developing a comprehensive understanding of how topological phases of matter behave not just in isolation but also in realistic noisy settings. Noise can destroy technologically useful topological features, but it can also be harnessed to engineer novel states of matter without analogs in isolated systems. This theoretical physics proposal operates at the interface of quantum many-body topology and open (noisy) systems with the goal of systematizing the patchwork of recent results on topological phases of open quantum systems, in particular formulating concrete representations of these phases and tools to probe their exotic features. In this pursuit, the proposal employs the powerful tools of tensor networks and topological quantum field theories, drawing on insights from disciplines ranging from condensed matter physics, quantum information theory, high energy physics, and mathematics. I will conduct my research at the University of Cambridge, with the guidance of Prof. Frank Verstraete, a leader in these areas. This project will broaden my technical expertise and strengthen my research profile, preparing me to become a tenured scholar.